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Particle decays and stability on the de Sitter universe

Jacques Bros, Henri Epstein, Ugo Moschella

TL;DR

The paper analyzes particle decays in de Sitter space at first order in perturbation theory, focusing on how de Sitter curvature alters standard Minkowski results. It develops a formalism based on adiabatic limits and Källén-Lehmann weights, revealing that particles with mass above a critical value can decay into heavier products (violating flat-space subadditivity), while below the critical mass the decay products obey quantization rules and can exhibit a form of stability. The authors compute explicit expressions for decay amplitudes in Minkowski space and extend them to de Sitter via principal/complementary series, deriving a closed-form lifetime formula in de Sitter that, strikingly, becomes independent of particle velocity in the appropriate regime. They also obtain explicit KL weights for two-body decays and discuss the Minkowski limit and the stability implications for complementary-series particles, highlighting fundamental differences from flat-space scattering and the absence of a conventional S-matrix in de Sitter space.

Abstract

We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the "phase space" coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.

Particle decays and stability on the de Sitter universe

TL;DR

The paper analyzes particle decays in de Sitter space at first order in perturbation theory, focusing on how de Sitter curvature alters standard Minkowski results. It develops a formalism based on adiabatic limits and Källén-Lehmann weights, revealing that particles with mass above a critical value can decay into heavier products (violating flat-space subadditivity), while below the critical mass the decay products obey quantization rules and can exhibit a form of stability. The authors compute explicit expressions for decay amplitudes in Minkowski space and extend them to de Sitter via principal/complementary series, deriving a closed-form lifetime formula in de Sitter that, strikingly, becomes independent of particle velocity in the appropriate regime. They also obtain explicit KL weights for two-body decays and discuss the Minkowski limit and the stability implications for complementary-series particles, highlighting fundamental differences from flat-space scattering and the absence of a conventional S-matrix in de Sitter space.

Abstract

We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the "phase space" coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass there is no such thing as particle stability, so that decays forbidden in flat space-time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.

Paper Structure

This paper contains 26 sections, 1 theorem, 225 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Free fields in Minkowski and de Sitter spacetimes
  4. Special features of free fields in de Sitter space-time
  5. More features common to Minkowski and de Sitter space-time
  6. Particle decays: general formalism
  7. Minkowski case
  8. Adiabatic limit: the Fermi golden rule
  9. Källén-Lehmann weights
  10. de Sitter case
  11. Adiabatic limit in the de Sitter case
  12. Closed FRW model:
  13. Flat FRW model:
  14. Källén-Lehmann weights
  15. Minkowskian limit
  16. ...and 11 more sections

Key Result

Lemma 6.1

provided and that the contour of integration in (r.26) separates the increasing and decreasing series of poles.

Figures (3)

  • Figure 1: Time-slices of the de Sitter spacetime in the closed and in the flat coordinate systems.
  • Figure 2: Graph of $G(x,\ \varepsilon_1,\ \varepsilon_2)$ when $g_1(x) = g_2(x) = \theta(x)\theta(1-x)$.
  • Figure 3: Graph of $G(x,\ \varepsilon_1,\ \varepsilon_2)$ when $g_1(x) = g_2(x) = \theta(1/2-|x|)$.

Theorems & Definitions (7)

  • Remark 2.1
  • Remark 2.2
  • Remark 4.1
  • Remark 6.1
  • Lemma 6.1: Barnes
  • Remark B.1
  • Remark C.1